Ionization

24 March 2003

Astronomy G9001 - Spring 2003

Prof. Mordecai-Mark Mac Low

Photoionization

• For hydrogenic ionic stages, the ionization cross-section (Dopita & Sutherland, 2003)

2, where 4i

i i

Fd F L d

h

18 2

2

3.56.3 10 cmH

i

Z

Recombination

• σrec can be derived from σi using detailed balance.

• For hydrogenic ions, the Gaunt factor gmf is

evaluated approximately in PPISM

( )

0

, ( )nrec

m n

m v vf v dv

2 3( , )

1 2mfi i

rec re

ghm v A

m v m

11 3 -1 2

( )1 2

0.72(1) 13 3 -1 4

Dopita & Sutherland (2003)

2.06 10 cm s, where .

For hydrogen, give

4.18 10 cm s 10 K

for 5,000 20,000

n im

Z h

T kT

T

T

Coronal Ionization Equilibrium

• collisional equilibrium between ion stages z and z+1

• Ionization fraction fz = nz/n depends only on T

1e z z e z zn n C T n n Tcoll. ioniz. rate (z to z+1)

rad. recom. rate (z+1 to z)

1 zz

z z

C Tf

f T

Ion Distribution in Coronal Equilibrium

Dopita & Sutherland 2003

I IIIII IX

VIII

VII

VI

VIV

Nebular Ionization Equilibrium

• photoionization equilibrium between ion stages z and z+1

• Ionization fraction depends on:

1z z e z zn L n n T photoioniz. rate (z to z+1)

rad. recom. rate (z+1 to z)

1

2

,

where the photoionization parameter

z z

z e z z

e

f

f n T T

L

n d

Kal

lman

& M

cCra

y 19

82

2e

L

n d

10 keV X-ray synch.spectrum

H II Regions• Observed H II regions limited:

– ionization bounded: all photons contained– density bounded: all atoms ionized

• The optical depth for ionization is tiny. – At edge, σ = 6.3 10-18 cm2, so if n = 1 cm-3

• Thus, density bounded H II regions have sharp edges

17

, so the mean free path, where 1, is

1.6 10 c 0.05 pcm

n dl

Ln

Strömgren Spheres• Two components to local ionizing flux near a

star– direct ionizing flux– diffuse flux from recombinations to ground state

• Calculate radius of ionized sphere in uniform ρ:– balance flux of ionizing photons through sphere S(r)

against recombinations to levels above ground α(2):

– Integrate over r until S(r) = 0 at r = rS

2 (2)( ) 4 e HdS r dr r xn n

3 (2)*

1/ 3

*(2)

40

3

3

4 ee H

HS S

Nr

n nr n n S N

Dynamical Solutions

• Temperature increases upon photoionization– Resulting pressure differential can only be

equalized by expansion of photoionized gas– When pressures balance, photoionized gas far less

dense than neutral gas

• Propagation of ionization front can be calculated by examining conservation equations, taking ΔT across front into account.

n n i i iv v J •flux of photons at front•mean mass per ion

Solving mass & momentum conservation forisothermal gas, we find:

1 222 2 2 2 2 2

2

4

2

n n n n n ii

n i

c v c v v c

c

in the frame of the ionization front:

For this to have a real solution, either

2

1 2 1 22 2 2 22 or 2

nn i i n i n i i n

i

cv c c c c v c c c

c

R type: ρi > ρn D type: ρi < ρn, shock precedes

Stages of Growth

• Ultracompact – less than 10”, associated with young stars

• Compact– more evolved, but still not nebular

• Standard– single stars or groups, show structure

• Giant– OB associations, early stages of superbubbles

Ultracompact HII Regions

• Defined to be less than about 10” in size

• Should be rare if H II regions expand at roughly 10 km/s

• Wood & Churchwell (1989) found 10x more than expected.

Confinement

• Three major mechanisms proposed– Bow shocks (Van Buren et al. 1990): ram pressure

of motion confines cometary regions.– Disk photoevaporation (Hollenbach et al. 1994):

dense disk provides mass source for core-halo– Pressure confinement (García-Segura & Franco,

1996): self-gravity increases core pressure, confining very small regions

Ionized Shell Instability

Garcia-Segura & Franco 1996

10,000 K 100 K

Escape of Ionizing Radiation from Galaxy

• Direct measurements (Hα) require a screen– High velocity clouds (Tufte et al. 1998, Bland-

Hawthorn et al. 1998)

– Magellanic Stream gas (Weiner & Williams 1996)

• Optical depth to ionizing radiation τ = 3– about 4% escape fraction– consistent with theoretical model of Domgörgen

& Mathis (1994)

Molecular Cloud Ionization

• Cosmic-ray ionization in presence of charged grains (Elmegreen 1979) gives x=ne/n

Elm

egre

en 1

979

1 2

5 -

6

1 2 1 2

1 37 -1

10

0.1 10 10 cs m

x

An

grain-sizefactor (2-5)

depletion

cosmic-rayioniz. rate

Assignments

• Flashcode registration

• Read sections 1-4 (quick start), and start looking at rest of manual

• Read sections I, II, VII, and one other (to be summarized) of Hollenbach & Tielens, Rev. Mod. Phys. 1999, 71, 173

MHD Courant Condition

• Similarly, the time step must include the fastest signal speed in the problem: either the flow velocity v or the fast magnetosonic speed vf

2 = cs2 + vA

2

2 2max , s A

xt

v c v

Lorentz Forces

• Update pressure term during source step

• Tension term drives Alfvén waves– Must be updated at same time as induction

equation to ensure correct propagation speeds– operator splitting of two terms

21 1 1

4 4 8B

B B B B

Added Routines

Ston

e &

Nor

man

199

2b

Flashcode History• Politics

– world historical– political– internal

• Components• Coding philosophy

– spaghetti (Fortran IV/66)– structured (Fortran 77)– modular (Fortran 90)

Flashcode Structure• setup preprocessor script

– reads configuration files • setups/ - problem specific

– Config file to generate Modules– init_block.F90 to initialize one block

•source/sites/ - location specific

– sets up makefiles and code for a particular problem, and a particular site.

• Compilation with gmake (can be parallel)

• Runtime input parameters in flash.par